3. An economist used the least squares procedure to fit a regression model of the form y₁ = B₁ + B₁x₁, +B₂x₂, +6,, where y is quantity demanded of a good (in million units), x, is price of the good (in cedis), x, is household income (in thousand cedis), and 8,~ N(0,0²). Tabulated below are sums obtained 8 sets of observations N Ev=483 2y =30567 Σx₁y=3068 Σ.χ. = 53 Σχ' = 365 Σx₂y=3795 Calculations have produced the following matrix 50.68462 -4.03077 0.33846 (x'x)' = Σ., = 60 2 x=472 Σχx, = 382 -3.18077] 0.23846 0.21346 a. Form the matrices: X'X and XY. b. Use (X'X) and X'Y to compute the OLS estimates for ,, i= 0,1,2. c. Write the fitted regression model and interpret the partial regression coefficients.
3. An economist used the least squares procedure to fit a regression model of the form y₁ = B₁ + B₁x₁, +B₂x₂, +6,, where y is quantity demanded of a good (in million units), x, is price of the good (in cedis), x, is household income (in thousand cedis), and 8,~ N(0,0²). Tabulated below are sums obtained 8 sets of observations N Ev=483 2y =30567 Σx₁y=3068 Σ.χ. = 53 Σχ' = 365 Σx₂y=3795 Calculations have produced the following matrix 50.68462 -4.03077 0.33846 (x'x)' = Σ., = 60 2 x=472 Σχx, = 382 -3.18077] 0.23846 0.21346 a. Form the matrices: X'X and XY. b. Use (X'X) and X'Y to compute the OLS estimates for ,, i= 0,1,2. c. Write the fitted regression model and interpret the partial regression coefficients.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![3. An economist used the least squares procedure to fit a regression model of the form
y₁ = B₁ + B₁x₁, +B₂x2, +,, where y is quantity demanded of a good (in million units),
x, is price of the good (in cedis), x₂ is household income (in thousand cedis), and
E, ~ N (0,0¹). Tabulated below are sums obtained 8 sets of observations
Σ.y=483
2y =30567
Ex₁y=3068
Σχ =53
Σχ = 365
Σx₂y=3795
Calculations have produced the following matrix
(x'x)' =
50.68462 -4.03077
0.33846
Ex=60
Σ.x = 472
Σxx, = 382
-3.18077]
0.23846
0.21346
a. Form the matrices: XX and X'Y.
b. Use (X'X) and X'Y to compute the OLS estimates for B₁, i = 0,1,2.
c. Write the fitted regression model and interpret the partial regression coefficients.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F996d0b28-9e82-4c62-83fd-d917b07e3e49%2F2f5f3ad8-58f4-48c3-b0b3-c0f9dba52f31%2F4r27p3b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. An economist used the least squares procedure to fit a regression model of the form
y₁ = B₁ + B₁x₁, +B₂x2, +,, where y is quantity demanded of a good (in million units),
x, is price of the good (in cedis), x₂ is household income (in thousand cedis), and
E, ~ N (0,0¹). Tabulated below are sums obtained 8 sets of observations
Σ.y=483
2y =30567
Ex₁y=3068
Σχ =53
Σχ = 365
Σx₂y=3795
Calculations have produced the following matrix
(x'x)' =
50.68462 -4.03077
0.33846
Ex=60
Σ.x = 472
Σxx, = 382
-3.18077]
0.23846
0.21346
a. Form the matrices: XX and X'Y.
b. Use (X'X) and X'Y to compute the OLS estimates for B₁, i = 0,1,2.
c. Write the fitted regression model and interpret the partial regression coefficients.
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